Question

Help please!

A collection of numbers M consists of all positive integers less than 20. If a collection of numbers N is a collection created by randomly choosing five numbers from M. Which of the following must be true about M?
i. The range must be at least 4
ii. The median must be at least 3
iii. The mean can be above 17

a. i only
b. ii only
c. i and ii only
d. i and iii only

Answers

  1. The answer choice which represents statements which are correct regarding the datasets described in the task content is; Choice C; i and ii only.

    Which of the answer choices represents statements which are true about the dataset described?

    It follows from the task content that the universal set M is described to contain all positive integers less than 20 while the collection of numbers N is created randomly by choosing five numbers from it.
    Consequently, it follows that since 5 number are to be chosen, the range must be at least 4 as this follows from the extreme case scenario of selecting consecutive numbers. Hence, statement i is correct.
    Also, the median must be at least three as the extreme case scenario in which numbers 1,2,3,4 and 5 are chosen still renders the median to be 3.
    The mean of the five numbers cannot be above 17 because, when when numbers, 15,16,17,18 and 19 are chosen, the mean is 17 and does not exceed 17. Hence, statement iii is incorrect.
    Read more on median and range;
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